Is it possible to stay in Face Mode when making loop cuts?
You can in a way.. In the 3d view header, hold Shift and click on the Edge and Face icons.  The only drawback to this is that you will be in both Edge and Face selection mode.

Also, the quickest way to switch selection modes in Blender is to use CtrlTab, (you can also hold Shift while selecting here too to get multiple selection modes, to leave a mode, do the same thing).